Rolling paper with bones
There are no skin weights on the plane so that would need to be fixed. The weight painting will take some time to do since you need to do it by hand. 

Also, you need to have much higher resolution on your mesh so it can deform properly and more bones to follow the curve to give a convincing result.

As a side note: It might be easier to solve this with a curve deformer directly attached to the mesh but I guess that you have reasons of doing this with bones.